On accelerating the convergence of the successive approximations method

In a previous paper of us, we have shown that no q-superlinear convergence to a fixed point \(x^\ast\) of a nonlinear mapping \(G\) may be attained by the successive approximations when \(G^\prime(x^\ast)\) has no eigenvalue equal to 0. However, high convergence orders may be attained if one conside...

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Bibliographic Details
Published inJournal of numerical analysis and approximation theory Vol. 30; no. 1
Main Author Emil Cătinaş
Format Journal Article
LanguageEnglish
Published Publishing House of the Romanian Academy 01.02.2001
Subjects
acceleration of the convergence of successive approximations
inexact Newton methods
quadratic convergence
successive approximations
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Summary:In a previous paper of us, we have shown that no q-superlinear convergence to a fixed point \(x^\ast\) of a nonlinear mapping \(G\) may be attained by the successive approximations when \(G^\prime(x^\ast)\) has no eigenvalue equal to 0. However, high convergence orders may be attained if one considers perturbed successive approximations. We characterize the correction terms which must be added at each step in order to obtain convergence with q-order 2 of the resulted iterates.
ISSN:2457-6794
2501-059X
DOI:10.33993/jnaat301-675